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arXiv · 1912.09690

Counting and equidistribution in quaternionic Heisenberg groups

Jouni Parkkonen·Frédéric Paulin
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Abstract

We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension $2$. We prove a Mertens counting formula for the rational points over a definite quaternion algebra $A$ over $\mathbb Q$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over $A$ in quaternionic Heisenberg groups.

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Jouni Parkkonen, Frédéric Paulin. 2019-12-20. Counting and equidistribution in quaternionic Heisenberg groups. https://arxiv.org/abs/1912.09690

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